Ordinal optimization: Soft optimization for hard problems

✍ Scribed by Ho Y.-C., Zhao Q.-C., Jia Q.-S.

• Publisher: Springer
• Year: 2007
• Tongue: English
• Leaves: 333
• Series: International Series on Discrete Event Dynamic Systems
• Category: Library

✦ Synopsis

Performance evaluation of increasingly complex human-made systems requires the use of simulation models. However, these systems are difficult to describe and capture by succinct mathematical models. The purpose of this book is to address the difficulties of the optimization of complex systems via simulation models or other computation-intensive models involving possible stochastic effects and discrete choices. This book establishes distinct advantages of the "softer" ordinal approach for search-based type problems, analyzes its general properties, and shows the many orders of magnitude improvement in computational efficiency that is possible.

✦ Table of Contents

Table of Contents......Page 7
Preface......Page 13
Acknowledgements......Page 15
I Introduction......Page 17
1 Two basic ideas of Ordinal Optimization (OO)......Page 23
2 Definitions, terminologies, and concepts for OO......Page 25
3 A simple demonstration of OO......Page 29
4 The exponential convergence of order and goal softening......Page 31
5 Universal alignment probabilities......Page 53
6 Deterministic complex optimization problem and Kolmogorov equivalence......Page 64
7 Example applications......Page 67
8 Preview of remaining chapters......Page 70
III Comparison of Selection Rules......Page 73
1 Classification of selection rules......Page 76
2 Quantify the efficiency of selection rules......Page 85
3 Examples of search reduction......Page 96
4 Some properties of good selection rules......Page 104
5 Conclusion......Page 106
IV Vector Ordinal Optimization......Page 109
1 Definitions, terminologies, and concepts for VOO......Page 110
2 Universal alignment probability......Page 115
3 Exponential convergence w.r.t order......Page 120
4 Examples of search reduction......Page 122
V Constrained Ordinal Optimization......Page 129
1 Determination of selected set in COO......Page 131
2 Example: Optimization with an imperfect feasibility model......Page 138
3 Conclusion......Page 140
VI Memory Limited Strategy Optimization......Page 141
1 Motivation (the need to find good enough and simple strategies)......Page 142
2 Good enough simple strategy search based on OO......Page 144
3 Conclusion......Page 151
VII Additional Extensions of the OO Methodology......Page 153
1 Extremely large design space......Page 154
2 Parallel implementation of OO......Page 159
3 Effect of correlated observation noises......Page 170
4 Optimal Computing Budget Allocation and Nested Partition......Page 175
5 Performance order vs. performance value......Page 184
6 Combination with other optimization algorithms......Page 191
VIII Real World Application Examples......Page 205
1 Scheduling problem for apparel manufacturing......Page 206
2 The turbine blade manufacturing process optimization problem......Page 223
3 Performance optimization for a remanufacturing system......Page 236
4 Witsenhausen problem......Page 248
1 Introduction to simulation......Page 269
2 Random numbers and variables generation......Page 271
3 Sampling, the central limit theorem, and confidence intervals......Page 276
5 Additional problems of simulating DEDS......Page 278
6 The alias method of choosing event types......Page 280
1 Elements of stochastic sequences and processes......Page 283
2 Modeling of discrete event simulation using stochastic sequences......Page 287
Appendix C Universal Alignment Tables for the Selection Rules in III......Page 295
1 True/False questions......Page 307
2 Multiple-choice questions......Page 309
3 General questions......Page 313
References......Page 321
H—N......Page 331
O—T......Page 332
U—Z......Page 333